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Solved: Estimating infinite sums Estimate the value of the
Chapter 10, Problem 35E(choose chapter or problem)
QUESTION:
35-38. Estimating infinite sums Estimate the value of the following convergent series with an absolute error less than \(10^{-3}\).
\(\sum_{k=1}^{\infty} \frac{(-1)^{k}}{k^{5}}\)
Questions & Answers
QUESTION:
35-38. Estimating infinite sums Estimate the value of the following convergent series with an absolute error less than \(10^{-3}\).
\(\sum_{k=1}^{\infty} \frac{(-1)^{k}}{k^{5}}\)
ANSWER:Problem 35E
Estimating infinite sums
Estimate the value of the following convergent series with an absolute error less than 10-3.
Solution:
Step 1
For the given convergent series we take .
The given series is an alternating series and that
a. and decreasing monotonically.